Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
286 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20266188 | C2 | semidirect |
| 4. #20266121 | C2 | semidirect |
| 5. #20266056 | C2 | semidirect |
| 6. #20266048 | C2 | semidirect |
| 25. #15692183 | C4 | semidirect |
| 26. #15692182 | C4 | semidirect |
| 27. #15692181 | C4 | semidirect |
| 28. #104×C101 | C4 | semidirect |
| 57. #13108058 | C2×C4 | semidirect |
| 61. C4×Dic101 | C2×C4 | semidirect |
| 63. M16×C101 | C2×C4 | semidirect |
| 64. C42×C101 | C2×C4 | semidirect |
| 131. C101 | #1860 | semidirect |
| 156. #104 | #87938 | semidirect |
| 179. M16 | C2×#87938 | semidirect |
| 195. C42 | C2×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266246 | 2 |
| #20266188 | 2 |
| #20266168 | 2 |
| #20266121 | 2 |
| #20266056 | 2 |
| #20266048 | 2 |
| #104×D101 | 2 |
| #1860 | 101 |